Find the zeros of the function. Enter the solutions from least to greatest. $h (x)=(-2x +3)(-x +3)$ $\text{lesser }x = $
For any two expressions $A$ and $B$ : If $A\cdot B=0$ then either $A=0$ or $B=0$. This is called the zero product property. In our case, $(-2x +3)(-x +3)=0$. So either $(-2x +3)=0$ or $(-x +3)=0$ : $\begin{aligned} (1)&&-2x +3&=0 \\\\ &&-2x&=-3 \\\\ &&x&=\dfrac{3}{2} \end{aligned}$ $\begin{aligned} (2)&&-x +3&=0 \\\\ &&-x &= -3 \\\\ &&x&=3 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= \dfrac{3}{2} \\\\ \text{greater } x &= 3 \end{aligned}$